Simplify; express your answer in exponential form. Assume $x\neq 0, n\neq 0$. $\dfrac{{(x^{4}n^{-1})^{-2}}}{{(x^{-2}n^{2})^{4}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(x^{4}n^{-1})^{-2} = (x^{4})^{-2}(n^{-1})^{-2}}$ On the left, we have ${x^{4}}$ to the exponent ${-2}$ . Now ${4 \times -2 = -8}$ , so ${(x^{4})^{-2} = x^{-8}}$ Apply the ideas above to simplify the equation. $\dfrac{{(x^{4}n^{-1})^{-2}}}{{(x^{-2}n^{2})^{4}}} = \dfrac{{x^{-8}n^{2}}}{{x^{-8}n^{8}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{-8}n^{2}}}{{x^{-8}n^{8}}} = \dfrac{{x^{-8}}}{{x^{-8}}} \cdot \dfrac{{n^{2}}}{{n^{8}}} = x^{{-8} - {(-8)}} \cdot n^{{2} - {8}} = n^{-6}$